Design of a Compact BLDC motor for Transient Applications

Y.K. Chin, W.M. Arshad, T. Bäckström & C. Sadarangani

Royal Institute of Technology (KTH) Department of Electrical Engineering

Teknikringen 33, SE-100 44 Stockholm, Sweden

Tel: + 46 8 790 7757 Fax: + 46 8 205 268 E-mail: Robert.chin@ekc.kth.se

URL: www.ekc.kth.se/eme/

Keywords: Brushless Drive, Thermal design, EMF. Abstract – Applications such as emergency breakers, protective devices in explosive environments, emergency exit openings etc. fall into a broad category that can be grouped under a general term transient applications. This paper presents a compact brushless permanent magnet (BLDC) motor design for those short time operations. Design procedures for both interior and exterior rotor BLDC configurations are described. Design analysis is verified by testing and building a prototype motor. It is found that the most critical design criterion is to avoid magnet demagnetisation. A thermal check on the design is always advisable although thermal loading is negligible. List of principal symbols Ephase = back EMF per phase, V T = rated torque, Nm I = phase current, A ωm = mechanical angular speed, rad/s kE = back-EMF constant, V.s/rad kT = torque constant, Nm/A kw = winding factor Z = total number of conductors p = number of poles Br = remanent magnetic flux density, T Bg = airgap flux density, T Biron = iron back saturation flux density, T g = physical airgap size, m ge = effective airgap, m lm = magnet thickness, m hrr = rotor back height, m hrs = stator back height, m L = machine active length, m D = airgap diameter,m Dr = rotor diameter, m hs = height of stator slot, m m = number of phases q = number of slots per pole-phase nphase = number of conductors per phase kslot = slot fill factor bts = width of stator teeth, m p = pole pitch, m s = slot pitch, m µ0 = permeability of air = 4π.·10-7 , Vs/Am µr = relative permeability, Aslot = slot area, m2 Aconductor = area of conductor, m2 Smax = maximum current loading allowed, A/m

I. INTRODUCTION

The majority of motors in the market are designed and used in either continuous or intermittent applications. It is possible in some cases to select an appropriate off-the-shelf motor for transient applications [1]. However, the choice for a suitable solution is limited. The induction motor can be an acceptable solution as long as the motor is not over-dimensioned [2]. A new motor design has to be considered if the off-the-shelf selection is not available or not compact enough. Therefore in this paper, a design approach on BLDC motors for transient applications is outlined. Selection of the BLDC motor configuration depends on the application requirements. This paper only deals with radial flux BLDC motor topology. Design procedures for both interior rotor and exterior rotor configurations, as shown in Fig. 1, are presented. In general, exterior-rotor brushless motors are used in continuous applications that require constant high to medium speed. Nonetheless, for an application requires rapid acceleration and deceleration of the load, it is desirable that the torque/inertia ratio is as high as possible [3]. In this case, the interior-rotor designs with high-energy magnets are preferred. A BLDC prototype motor presented in this paper is an interior-rotor design, specifically for short time operation. Measurement results and thermal-check approaches on the prototype design are also described.

Fig. 1: Brushless permanent magnet motor: a) Exterior-rotor; b) Interior-rotor.

a) b)

II. INTERIOR-ROTOR BLDC DESIGN The number of phases, poles, stator slots as well as winding configuration must be selected based on the application requirements. The choice of pole number depends upon many factors such as inertia requirements, magnet material, effect of cogging and rotation speed etc. [3]. The required thickness of the stator back is reduced by one half if the number of poles is doubled, so is the case with the rotor back height (1). For a given magnetic and electric loading with a specified rotor diameter, the overall machine diameter can be reduced by increasing the pole number.

iron

rgrsrr Bp

DBhh

⋅⋅⋅

⋅⋅==

22π (1)

With a certain magnet radial thickness selected, the airgap flux density Bg can be calculated by (2) as described in [4],

m

er

rg

lg

BB⋅+

=µ1

(2)

and effective airgap (ge) is defined as,

r

mce

lgg

µ+= (3)

where gc is the airgap with the slotting being considered. The stator inner diameter (Dis) is then,

)(2 glDD mris +⋅+= (4) The width of the stator teeth is found by using (5),

iron

gists BQ

BDb

⋅

⋅⋅=π (5)

For a compact motor design, a high surface current loading (S1) is very desirable. However, the current loading must always be smaller than the maximum allowed current loading (Smax) given by (7), to avoid the demagnetisation of the permanent magnet.

⋅⋅⋅⋅⋅

⋅

=

wg kLBDTS 21

223

π [A/m] (6)

( )

pD

BBkgSS Dgwe ⋅

⋅⋅⋅

−⋅⋅⋅=<

αµ sin22

0

1max1

[A/m] (7)

where BD is the demagnetisation flux density limit and α is half of the magnet span in electric degrees. The active length of the machine is calculated as,

⋅⋅⋅⋅

=1

2

3SBD

TLgπ

(8)

The number of conductors per slot is found as,

qp

Zns ⋅⋅=

3 (9)

where Z is the total number of conductors, it can be obtained by (10) for a three-phase machine.

wg kBILDTZ

⋅⋅⋅⋅⋅

=3 (10)

In addition, the torque constant kT can be derived from (10) as,

[ ]wgT kBLDZITk ⋅⋅⋅⋅⋅==

31 [Nm/A] (11)

The back-EMF Ephase of the motor can be approximated by (12),

gwsphase BkLDnqE ⋅⋅⋅⋅⋅⋅= ω (12)

The area of stator slot is found with a certain slot height (hs) selected,

sts

iss

isslot hb

Dh

DQ

A ⋅−

−

+⋅=

22

22π (13)

The copper area and area of single conductor in the slot can simply be found with (14) and (15) respectively,

fillslotcu kAA ⋅= (14)

s

cuconductor n

AA = (15)

Lastly, the stator outer diameter Dos is then,

( )rssisos hhDD +⋅+= 2 (16) Fig. 2: Copper area available in the stator slot.

Aconductor

Aslot Acu

hS

τs

The external dimension of the machine is dependent on the stator frame and end-windings. The length of the end winding is dependent upon the winding configuration.

III. EXTERIOR-ROTOR BLDC DESIGN The design procedure for the exterior-rotor topology is very similar to the one described for the interior-rotor design. However, as it has shown in Fig. 1(a), the machine dimensions are different. In the following, only these differences are highlighted. With a specified rotor diameter, the pole pitch of the exterior-rotor design is calculated as,

( )p

hD rrorp

⋅−⋅=

2πτ (17)

where hrr is obtained as,

iron

gprr B

Bh

⋅

⋅=

2τ (18)

Combining of (17) and (18),

⋅+

⋅=

iron

g

orp

BB

p

Dπ

πτ

(19)

The inner diameter of the rotor Dir and outer stator Dos are found as,

)(2 mrrorir lhDD +⋅−= (20)

gDD isos ⋅−= 2 (21) The stator teeth at the arigap is then,

iron

gosts Bp

BDb

⋅

⋅⋅=π (22)

The stator back height is designed to carry the same flux as the rotor back, as shown in (18). In contrast to the interior-rotor design, the diameter of the stator is limited due to the space available. With the constant stator teeth, the height of the stator slot hs is,

⋅⋅

−=π22

tsoss

bQDh (23)

The available copper area in the stator slot is then,

( ) ( )[ ]

⋅−⋅−−⋅

⋅⋅= tsssososfillcu bhhDD

QkA 22 2

4π (24)

Fig. 3: Simple schematic of exterior-rotor design stator

The exterior-rotor design follows the same step as that of the interior-rotor design as far as the electric design is concerned.

IV. THERMAL CHECK Despite the fact that the thermal loading is not a critical factor in the design for transient application, a thermal check on the design is nevertheless advisable. Most of the heat is generated as the conducting loss in the stator conductors. It is therefore sufficient to analyse the stator structure only. The thermal model for the machine stator is shown in Fig. 4. Stator is divided into three thermal regions as slot, teeth, and stator back. Thermal capacitance has to be taken into account for the transient applications. To calculate the temperature rise in respective regions, differential equations (25, 26, 27) are derived from the equivalent circuit. Adiabatic conditions are assumed.

1

12121 )(C

YTTPdt

dT cu ⋅−+= (25)

( ) ( )2

232312212

CYTTYTTP

dtdT teeth ⋅−+⋅−+

= (26)

( )3

23323

CYTTP

dtdT fe ⋅−+

=

(27)

Fig. 4: Thermal equivalent circuit of the stator.

hs

bts

Aslot

Dos

Pcu = copper losses, W Pteeth, Pback = iron losses in stator teeth and back, W Ci = thermal capacitance, W/K Yij = thermal conductance between region i and j, Ws/K

Fig. 5: Stator thermal regions: teeth, windings and back.

V. PROTOTYPE MOTOR A. Design A prototype motor for transient applications based on the design procedures described in II has been built. The prototype is shown in Fig. 6. The stator consists of 60 0.5mm DK-70 steel laminations stacked together. Neodymium-Iron-Boron magnets (Br ~ 1.1T) are used and glued on the rotor shaft. Bandage around the magnets is found not necessary. Moreover, magnets are skewed by one slot pitch to minimize the cogging torque. The dimensions and properties of the prototype are presented in TABLE I. TABLE I. Dimensions and properties of the prototype motor.

PARAMETER SYMBOL FIGURE

Number of phases m 3 Number of poles p 4 Number of slots Q 12 Airgap g 0.5 mm Rated torque T 0.4 Nm Airgap flux density Bg ~ 0.4 T Rated speed ωm 7500 RPM Back-EMF Eph 11.9 V Rotor diameter Dr 20 mm Airgap diameter D 22.5 mm Stator inner diameter Dis 23 mm Stator outer diameter Dos 52.8 mm Tooth width bts 3 mm Rotor back height hrr 4.4 mm Stator back height hrs 4.4 mm Magnet thickness lm 1 mm Copper area Acu ~ 32.5 mm2

No. of conduc. / slot ns 28 Slot height hs 10 mm Active motor length L 30 mm End winding length Lend 9 mm Current density J ~ 10 A/mm2

Max. temperature Tmax ~ 61.2 oC Diameter of conduc. Aconductor 1.1 mm Current loading S1 47.5 kA/m Max. current loading Smax 85.1 kA/m Centrifugal force on magnets Fcentrifugal 7.6 N

Mass of copper Mcopper ~ 170 g Mass of magnet Mmagnet ~ 144 g Mass of iron Miron ~ 310 g

Fig. 6: BLDC motor prototype: a) Transversal view; b) Longitudinal View. B. Measurements The back EMF of the prototype is measured and is illustrated in Fig. 7. The phase current waveform is observed as shown in Fig. 8. The machine constants, kT and kE, are defined as,

ITkT = (28)

m

LLE

Ek

ω= (29)

where ELL is the line-to-line back-EMF. The constants can also be calculated directly [3] from the motor dimensions and the magnet properties by (30). In an ideal case with no saturation, no resistance and no voltage-drops in the controller, the two constants are equal.

πα ⋅

⋅Φ⋅==

pZkkk g

wTE 32 (30)

where Φg is the airgap flux per pole due to the magnet,

Bp

LDg ⋅

⋅⋅⋅

⋅=Φ2

πα (31)

Fig. 9 and Fig. 10 show the measurements for kE and kT respectively, and the best-fit line drawn from graph is used for calculating kE and kT. Comparisons of machine constants obtained by measurements and calculation are presented in TABLE II.

a)

b)

Fig. 7: Back-EMF waveforms of the prototype motor.

Fig. 8: Phase current waveform with the Hall-switch signal.

VI. CONCLUSIONS

It is possible to obtain a compact motor design solution for transient applications with the proposed procedure. It is found that the magnet demagnetization is the most critical design criterion. A thermal check on the obtained design is nevertheless suggested, although the thermal loading is negligible. The BLDC motor prototype built for short time operations as a design example shows satisfactory results. The measured machine constants, kE and kT, agrees with the calculated values. A brushless permanent magnet motor can be one of the preferred solutions from a cost and design effort perspective, when a new motor design is required for transient applications.

TABLE II. Comparison of machine constants, kE and kT: a) Measured; b) Calculated.

MEASURED CALCULATION

kE [Vs/rad] ~ 0.042 0.04

kT [Nm/A] ~ 0.044 0.04

The graph of back emf versus speed

0

5

10

15

20

25

30

0 750 1500 2250 3000 3750 4500 5250 6000 6750

Speed (rpm)

Back

em

f (vo

lts)

Fig. 9: Measurements for kE.

The graph of torque versus current

-0,08

-0,03

0,02

0,07

0,12

0,17

0,22

0,27

0,32

0 1 2 3 4 5 6 7 8

DC Current (A)

Torq

ue (N

m)

Fig. 10: Measurements for kT.

REFERENCES

[1] Chandur Sadarangani, Electrical machines – Design and Analysis of Induction and Permanent Magnet Motors, KTH 2000

[2] Arshad, W.M., Chin, Y.K., Soulard, J., Bäckström, T., Östlund, S., Sadarangani, C., On Finding Compact Motor Solutions for Transient Applications, IEMDC’2001, Cambridge, MA USA.

[3] Hendershot, J.R. and Miller, T.J.E., Design of Brushless Permanent-Magnet Motors, Magna Physics Publishing, 1994, Oxford.

[4] Sebastian, T., Slemon, G.R., Rahman, M.A., Design Considerations for Variable Speed Permanent Magnet Motors, Part 3. p.p. 1099~1102, ICEM, September, 1986.